0,2

This is a generalization of A114043, which can be viewed as the number of intersections of a halfspace with the n X n grid (divided by 2).

a(3) = 214 (X's indicate points in intersection):

... X.. .X. ... XX. X.. X.. X.. XXX XX. XX. XX. X.. X.. .X. .X.

... ... ... .X. ... .X. ..X ... ... X.. .X. ..X .XX .X. .X. XX.

... ... ... ... ... ... ... .X. ... ... ... ... ... ..X .X. ...

-1- -4- -4- -1- -8- -4- -8- -8- -4- -4- -8- -8- -8- -2- -2- -4-

XXX XXX XX. XX. XX. XX. .X. X.. XXX XXX XX. XX. XX. XX. .X. XX.

X.. .X. XX. .X. .XX .X. XXX .XX XX. .X. .XX .XX XXX XX. XXX .X.

... ... ... .X. ... ..X ... .X. ... .X. ..X .X. ... ..X .X. .XX

-8- -4- -4- -8- -8- -8- -4- -4- -8- -4- -4- -8- -8- -4- -1- -4-

XXX XXX XXX XX. XX. XXX XXX XX. XXX XXX

XXX XX. XX. XXX XXX XXX XXX XXX XXX XXX

... X.. .X. .X. ..X X.. .X. .XX XX. XXX

-4- -4- -8- -4- -8- -8- -4- -2- -4- -1-

Cf. A114043.

Sequence in context: A138429 A087923 A004121 this_sequence A012056 A062971 A012164

Adjacent sequences: A114528 A114529 A114530 this_sequence A114532 A114533 A114534

nonn

David Applegate (david(AT)research.att.com), Feb 24 2006